Red Perimeter 4 – Inner Units

Probability Level 1

For a given n × n n \times n square with the perimeter painted red, how many unit squares will have no paint on them at all?

( n − 1 ) 2 (n-1)^2 n 2 − 1 n^2 -1 n 2 − 28 n^2 - 28 ( n − 2 ) 2 (n-2)^2

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Arron Kau by Arron Kau

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5 solutions

Nmber of corner squares =4(N-1). So ans : n^2-4n+4=(n-2)^2

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Prajwal Kavad
May 24, 2014

(n-2)^2 is the answer

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Krishna Garg
May 21, 2014

Looking to the figure,upper next enclosed area( not covered with red lines)will be n-2 so Area of this will be (n-2)square. K.K.GARG,India

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Mona Mazen
May 18, 2014

n is number of squares on each side. n-2 gives the number of squares on the inner square that has no red on any of its squares. (n-2)(n-2) gives the total number of squares in the inner square.

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Shohag Hossen
May 15, 2014

(n-2)^2 is the correct answer, (number of corner is) 4 + (one side) 4(n - 2) + ans = n n; ans = n n - 4n +4; ans = (n-2)*(n-2)

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